For example the statement "d2 is the weekday following d1" can be seen as a truth function associating to each tuple (d2, d1) the value true or false. The extension of this truth function is, by convention, the set of all such tuples associated with the value true, i.e.

If the values 0 and 1 in the range of a characteristic function are identified with the values false and true, respectively – making the characteristic function a predicate – , then for all relations R and predicates the following two statements are equivalent: